Realization of Periodic Functions by Self-stabilizing Population Protocols with Synchronous Handshakes

  • Anissa LamaniEmail author
  • Masafumi Yamashita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10071)


We consider in the following the problem of realizing periodic functions by a collection of finite state-agents that cooperate by interacting with each other. More formally, given a periodic non-negative integer function f that maps the set of non-negative integers \(\mathbf{N}\) to itself, we aim in this paper at designing a distributed protocol with a state set Q and a subset \(S \subseteq Q\), such that, for any initial configuration \(C_0\), with probability 1, there are a time instant \(t_0\) and a constant \(d \in \mathbf{N}\) satisfying \(f(t+d) = \nu _S(C_t)\) for all \(t \ge t_0\), where \(\nu _S(C)\) is the number of agents with a state in S in a configuration C. The model that we consider is a variant of the population protocol (PP) model in which we assume that each agent is involved in an interaction at each time instant t, hence the notion of synchronous handshakes. These additional assumptions on the model are necessary to solve the considered problem. We also assume that the interacting pairs are matched uniformly at random.


Self-organizing systems Self-stabilization Clock synchronization Oscillators Group construction Population protocol Uniform scheduler 


  1. 1.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: PODC, pp. 290–299 (2004)Google Scholar
  2. 2.
    Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. TAAS, 3(4), 13:1–13:28 (2008)Google Scholar
  3. 3.
    Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: A time-optimal self-stabilizing synchronizer using A phase clock. IEEE Trans. Dependable Secure Comput. 4(3), 180–190 (2007)CrossRefGoogle Scholar
  4. 4.
    Beauquier, J., Burman, J.: Self-stabilizing synchronization in mobile sensor networks with covering. In: Rajaraman, R., Moscibroda, T., Dunkels, A., Scaglione, A. (eds.) DCOSS 2010. LNCS, vol. 6131, pp. 362–378. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13651-1_26 CrossRefGoogle Scholar
  5. 5.
    Beauquier, J., Burman, J.: Self-stabilizing mutual exclusion and group mutual exclusion for population protocols with covering. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 235–250. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-25873-2_17 CrossRefGoogle Scholar
  6. 6.
    Boulinier, C., Petit, F., Villain, V.: When graph theory helps self-stabilization. In: PODC, pp. 150–159 (2004)Google Scholar
  7. 7.
    Cai, S., Izumi, T., Wada, K.: How to prove impossibility under global fairness: on space complexity of self-stabilizing leader election on a population protocol model. Theory Comput. Syst. 50(3), 433–445 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Cooper, C., Lamani, A., Viglietta, G., Yamashita, M., Yamauchi, Y.: Constructing self-stabilizing oscillators in population protocols. In: Pelc, A., Schwarzmann, A.A. (eds.) SSS 2015. LNCS, vol. 9212, pp. 187–200. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-21741-3_13 CrossRefGoogle Scholar
  9. 9.
    Couvreur, J., Francez, N., Gouda, M.G.: Asynchronous unison (extended abstract). In: ICDCS, pp. 486–493 (1992)Google Scholar
  10. 10.
    Czyzowicz, J., Ga̧sieniec, L., Kosowski, A., Kranakis, E., Spirakis, P.G., Uznański, P.: On convergence and threshold properties of discrete Lotka-Volterra population protocols. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9134, pp. 393–405. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-47672-7_32 Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of InformaticsKyushu UniversityFukuokaJapan

Personalised recommendations